Question

tanα的导数

Answer 1

sec²α

tanα的求导过程如下：

(tanα)'

=(sinα/cosα)'

=[(sinα)'cosα-(cosα)'sinα]/cos^2 α

=[cos^2 α+sin^2 α]/cos^2 α

=1/cos^2 α

=sec²α

扩展资料：

用u和v表示两个函数，则u/v)的求导过程如下：

(u/v)'=[u*v^(-1)]' 

=u' * [v^(-1)] +[v^(-1)]' * u

= u' * [v^(-1)] + (-1)v^(-2)*v' * u

=u'/v - u*v'/(v^2)

通分,易得：(u/v)=(u'v-uv')/v²

参考资料：百度百科-求导